Table of Content

18 October 2006, Volume 27 Issue 10

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Articles

SUPPORT VECTOR MACHINE FOR STRUCTURAL RELIABILITY ANALYSIS

LI Hong-shuang;LÜZhen-zhou;YUE Zhu-feng

2006, 27(10):  1295-1303 .  doi:10.1007/s10483-006-1001-z

Abstract ( 1440 )   PDF (256KB) ( 528 )  

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Support vector machine (SVM) was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method (FORM) and the Monte Carlo simulation (MCS). As a classification method where the underlying structural risk minimization inference rule is employed, SVM possesses excellent learning capacity with a small amount of information and good capability of generalization over the complete data. Hence, two approaches, i.e. SVM-based FORM and SVM-based MCS, were presented for the structural reliability analysis of the implicit limit state function. Compared to the conventional response surface method (RSM) and the artificial neural network (ANN), which are widely used to replace the implicit state function for alleviating the computation cost, the more important advantages of SVM are that it can approximate the implicit function with higher precision and better generalization under the small amount of information and avoid the "curse of dimensionality". The SVM-based reliability approaches can approximate the actual performance function over the complete sampling data with the decreased number of the implicit performance function analysis (usually finite element analysis), and the computational precision can satisfy the engineering requirement, which are demonstrated by illustrations.

ANALYTICAL SOLUTION FOR FIXED-FIXED ANISOTROPIC BEAM SUBJECTED TO UNIFORM LOAD

DING Hao-jiang;HUANG De-jin;WANG Hui-ming

2006, 27(10):  1305-1310 .  doi:10.1007/s10483-006-1002-z

Abstract ( 1501 )   PDF (152KB) ( 1229 )  

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The analytical solutions of the stresses and displacements were obtained for fixed-fixed anisotropic beams subjected to uniform load. A stress function involving unknown coefficients was constructed, and the general expressions of stress and displacement were obtained by means of Airy stress function method. Two types of the description for the fixed end boundary condition were considered. The introduced unknown coefficients in stress function were determined by using the boundary conditions. The analytical solutions for stresses and displacements were finally obtained. Numerical tests show that the analytical solutions agree with the FEM results. The analytical solution supplies a classical example for the elasticity theory.

OSCILLATION BEHAVIOR OF SOLUTIONS FOR EVEN ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

T. Candan

2006, 27(10):  1311-1320 .  doi:10.1007/s10483-006-1003-1

Abstract ( 1332 )   PDF (144KB) ( 466 )  

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Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.

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ZHAO Hai-bo;ZHENG Chu-guang

2006, 27(10):  1321-1332 .  doi:10.1007/s10483-006-1004-z

Abstract ( 1505 )   PDF (310KB) ( 535 )  

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EXACT SOLUTION OF LARGE DEFORMATION BASIC EQUATIONS OF CIRCULAR MEMBRANE UNDER CENTRAL FORCE

HAO Ji-ping;YAN Xin-li

2006, 27(10):  1333-1337 .  doi:10.1007/s10483-006-1005-1

Abstract ( 1682 )   PDF (117KB) ( 655 )  

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Exact solution of the nonlinear boundary value problem for the basic equation and boundary condition of circular membrane under central force was obtained by using new simple methods. The existence and uniqueness of the solution were discussed by using of modern immovable point theorems. Although specific problem is treated, the basic principles of the methods can be applied to a considerable variety of nonlinear problems.

HIGH PERFORMANCE SPARSE SOLVER FOR UNSYMMETRICAL LINEAR EQUATIONS WITH OUT-OF-CORE STRATEGIES AND ITS APPLICATION ON MESHLESS METHODS

YUAN Wei-ran;CHEN Pu;LIU Kai-xin

2006, 27(10):  1339-1348 .  doi:10.1007/s10483-006-1006-1

Abstract ( 1494 )   PDF (163KB) ( 771 )  

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A new direct method for solving unsymmetrical sparse linear systems(USLS) arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin (MLPG) method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.

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Emin Özyilmaz

2006, 27(10):  1349-1360 .  doi:10.1007/s10483-006-1007-1

Abstract ( 1314 )   PDF (181KB) ( 723 )  

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DOUBLE-MEDIUM CONSTITUTIVE MODEL OF GEOLOGICAL MATERIAL IN UNIAXIAL TENSION AND COMPRESSION

LIU Xiao-li;WANG Si-jing;WANG En-zhi;XUE Qiang

2006, 27(10):  1361-1372 .  doi:10.1007/s10483-006-1008-z

Abstract ( 1451 )   PDF (273KB) ( 607 )  

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Based on elasto-plasticity and damage mechanics, a double-medium constitutive model of geological material under uniaxial tension and compression was presented, on the assumption that rock and soil materials are the pore-fracture double-medium, and porous medium has no damage occurring, while fracture medium has damage occurring with load. To the implicit equation of the model, iterative method was adopted to obtain the complete stress-strain curve of the material. The result shows that many different distributions (uniform distribution, concentrated distribution and random distribution) of fractures in rock and soil material are the essential reasons of the daedal constitutive relations. By the reason that the double-medium constitutive model separates the material to be porous medium part, which is the main body of elasticity, and fracture medium part, which is the main body of damage, it is of important practical values and theoretical meanings to the study on failure of rock and soil or materials containing damage.

SECOND-ORDER MOMENT MODEL FOR DENSE TWO-PHASE TURBULENT FLOW OF BINGHAM FLUID WITH PARTICLES

ZENG Zhuo-xiong;ZHOU Li-xing;LIU Zhi-he

2006, 27(10):  1373-1381 .  doi:10.1007/s10483-006-1009-z

Abstract ( 1633 )   PDF (233KB) ( 587 )  

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The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

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LI Wen-cheng;DENG Zi-chen;HUANG Yong-an

2006, 27(10):  1383-1390 .  doi:10.1007/s10483-006-1010-z

Abstract ( 1635 )   PDF (326KB) ( 491 )  

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RESISTANCE EFFECT OF ELECTRIC DOUBLE LAYER ON LIQUID FLOW IN MICROCHANNEL

GONG Lei;WU Jian-kang

2006, 27(10):  1391-1398 .  doi:10.1007/s10483-006-1011-1

Abstract ( 1548 )   PDF (180KB) ( 900 )  

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Poisson-Boltzmann equation for EDL (electric double layer) and Navier-Stokes equation for liquid flows were numerically solved to investigate resistance effect of electric double layer on liquid flow in microchannel. The dimension analysis indicates that the resistance effect of electric double layer can be estimated by an electric resistance number, which is proportional to the square of the liquid dielectric constant and the solid surface zeta potential, and inverse-proportional to the liquid dynamic viscosity, electric conductivity and the square of the channel width. An "electric current density balancing" (ECDB) condition was proposed to evaluate the flow-induced streaming potential, instead of conventional "electric current balancing" (ECB) condition which may induce spurious local backflow in neighborhood of the solid wall of the microchannel. The numerical results of the flow rate loss ratio and velocity profile are also given to demonstrate the resistance effect of electric double layer in microchannel.

APPLICATION OF WU ELIMINATION METHOD TO CONSTRAINED DYNAMICS

JIA Yi-feng;CHEN Yu-fu;XU Zhi-qiang

2006, 27(10):  1399-1408 .  doi:10.1007/s10483-006-1012-y

Abstract ( 1440 )   PDF (171KB) ( 951 )  

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The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics were considered. A new algorithm was presented for solving constraints based on Wu elimination method. The new algorithm does not need to calculate the rank of Hessian matrix and determine the linear dependence of equations, so the steps of calculation decrease greatly. In addition, the expanding of expression occurring in the computing process is smaller. Using the symbolic computation software platform, the new algorithm can be executed in computers.

CAUCHY PROBLEM OF ONE TYPE OF ATMOSPHERE EVOLUTION EQUATIONS

HE Juan-xiong;HE You-hua

2006, 27(10):  1409-1416 .  doi:10.1007/s10483-006-1013-y

Abstract ( 1334 )   PDF (159KB) ( 811 )  

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One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, (i) the inertial force has no influence on the criterion of the well-posed Cauchy problem; (ii) the compressibility plays no role on the well-posed condition of the Cauchy problem of the viscid atmosphere equations, but changes the well-posed condition of the viscid atmosphere equations; (iii) this type of atmosphere evolution equations is ill-posed on the hyperplane t=0 in spite of its compressibility and viscosity; (iv) the Cauchy problem of compressible viscosity atmosphere with still initial motion is ill-posed.

NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

DU Guo-jun;MA Jian-qing

2006, 27(10):  1417-1424 .  doi:10.1007/s10483-006-1014-y

Abstract ( 1660 )   PDF (158KB) ( 740 )  

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Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.

STATIC ANALYSIS OF CABLE STRUCTURE

HUANG Yan;LAN Wei-ren

2006, 27(10):  1425-1430 .  doi:10.1007/s10483-006-1015-y

Abstract ( 1694 )   PDF (136KB) ( 1313 )  

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Based on the nonlinear geometric relation between strain and displacement for flexible cable, the equilibrium equation under self-weight and influence of temperature was established and an analytical solution of displacement and
tension distribution defined in Eulerian coordinate system was accurately obtained. The nonlinear algebraic equations caused by cable structure were solved directly using the modified Powell hybrid algorithm with high precision routine DNEQNE of Fortran. For example, a cable structure consisting of three cables jointly supported by a vertical spring and all the other ends fixed was calculated and compared with various methods by other scholars.

SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD

LIU Zhi-fang;ZHANG Shan-yuan

2006, 27(10):  1431-1437 .  doi:10.1007/s10483-006-1016-y

Abstract ( 1529 )   PDF (127KB) ( 720 )  

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A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.